Differencing Nonstationary Series Requires Testing the Result
Summary
The discussion considers whether lower Dickey–Fuller p-values at a higher sampling frequency imply that differencing will make a Treasury-yield series stationary. The answer is no: p-values for the original series do not establish the stationarity of a differenced series. The differenced data must itself be tested with a unit-root test.
Differencing is a common first step when a series appears nonstationary, and the number of differences needed for stationarity is related to its integration order. But the document cautions against repeatedly differencing simply to satisfy modeling assumptions. It describes a general econometric practice rather than presenting test results for the cited yield data, and it does not discuss test specification or other ways of modeling nonstationarity.
Key ideas
- A unit-root test on the original series cannot determine whether its differenced values are stationary.
- Test the differenced series directly before concluding that differencing resolved nonstationarity.
- The number of differences needed to achieve stationarity relates to a series’ integration order.
- Repeated differencing can be driven by modeling convenience and should not be treated as an automatic remedy.
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Full text
# Dickey Fuller test of stationarity differenced data
# Dickey Fuller test of stationarity differenced data
In this case study on treasury yeilds from MIT, I have a question on page 11-12. He uses this data
> getYahooData("^TNX", start=20000101, end=20130531)
His logic on page 11 is this
- "only daily is close to being stationary" (I get this)
- "we observe lower p value when higher freq frequency" (I see this since p-value daily < p-value monthly)
- "so stronger time series structure at higher freq, hence we diffrence the data"
for that data, we reject H0: non-stationary.
I want to understand how he can go from seeing the p-values are lower for daily (closer to stationary) into knowing that differenced data will reject H0.
## Answer by Jacob Amos (score 1, accepted)
https://quant.stackexchange.com/a/24667
As far as I know, it's impossible to know that the differenced data will stationary (reject H0). That being said, when we have a time series that is non-stationary, the first thing a lot of econometricians do is difference the data. Still stationary? Difference it again!
After skimming the reference you gave, I don't think he's making the assumption that the first-differenced series will be stationary. My guess is that he knows that to be the case beforehand and is simply demonstrating it. Unless I'm missing something, it's not possible to know a non-stationary time series will become stationary after differencing it once without performing the unit root test on the differenced data.
(FYR: How many times you have to difference something until it's stationary gives you the order to which the series is said to be integrated.)
At the risk of editorializing, I once had a statistics professor whose biggest complaint about time series & econometrics was an apparent obsession with differencing data just to make the math work.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.